Component Adaptive Life Management

ABSTRACT

A framework for adaptively managing the life of components. A sensor provides non-destructive test data obtained from inspecting a component. The inspection data may be filtered using reference signatures and by subtracting a baseline. The filtered inspection data and other inspection data for the component is analyzed to locate flaws and estimate the current condition of the component. The current condition may then be used to predict the component&#39;s condition at a future time or to predict a future time at which the component&#39;s condition will have deteriorated to a certain level. A current condition may be input to a precomputed database to look up the future condition or time. The future condition or time is described by a probability distribution which may be used to assess the risk of component failure. The assessed risk may be used to determine whether the part should continue in service, be replaced or repaired. A hyperlattice database is used with a rapid searching method to estimate at least one material condition and one usage parameter, such as stress level for the component. The hyperlattice is also used to rapidly predict future condition, associated uncertainty and risk of failure.

RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.61/184,672, filed on Jun. 5, 2009, the entire teachings of whichapplication are incorporated herein by reference.

GOVERNMENT SUPPORT

The invention was supported, in whole or in part, by a grant NNX09CE84Pfrom NASA and by a grant N68335-08-C-0008 from the U.S. Navy. TheGovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

There are many applications where using a component to failure isunacceptable, and thus the component must be replaced when the risk offailure is too high. The decision of when to retire a component is atradeoff between at least the cost of replacement and the risk offailure should the part continue to be used.

Component failure is preceded by deterioration in the condition of thecomponent. Deterioration of a component's condition is caused by thedevelopment and growth of flaws in the component. Flaws for metals mayinclude cracks, microcracks, inclusions, residual stress variations,microstructure variations, mechanical damage such as dents andscratches, corrosion pits, and machining effects. Flaws for compositesmight include fiber damage, bridging, impact damage, disbands, anddelaminations. Flaws may originate during manufacture or develop oncethe component is in service. While in service the component may beexposed to operating conditions that lead to the development and/orfurther growth of the flaw. Different types of components may be moresensitive to different types of loads. Operating conditions that mayaffect the condition of a component may include temperature, temperaturevariation (e.g., freeze-thaw cycles), acceleration, vibration, voltage,pressure, rotational speed, mechanical stress, static loading, dynamicloading, impact events, and any other physical process that contributesto the development and/or growth of component flaws.

In many applications a component is in use intermittently and thus theoperating conditions may not be persistent in time. Accordingly, thein-service time of a component may be measured in effective usagecycles, rather than in time directly. For example, an airplane componentmay be exposed to adverse operating conditions principally during eachtake off and landing cycles (or ground-air-ground, “GAG”, cycles). Theoperating environment while the aircraft is grounded or cruising mayhave significantly less contribution to flaw growth than the operatingconditions during takeoff and landing. Accordingly, a suitablein-service time unit may be takeoff/land cycles. Though, other suitablemeasures of in-service time may be used.

Safe life models have been used to predict the life of components. Thesemodels consider the operating conditions that cause damage to acomponent and estimate the intensity of these conditions while thecomponent is in service. Assuming an initial flaw site, safe life modelspredict the growth of the flaw as the component is exposed to worst caseoperating conditions. Component failure may be defined, for example, bya point in the growth of a flaw in the component at which the componentmay no longer serve its intended purpose. The component may be replacedwhen the service time of the component reaches some fraction of theservice time at which the component is predicted by the safe life modelsto fail (e.g. 50%).

Periodic inspection of components may also be used to detect flaws. Theinspection may not only look for the presence of flaws but also tocharacterize the flaw with one or more features. For example, a crack ina component may be characterized by the crack's length. Component flawgrowth models may then be used to predict, for example, the likelihoodthe flaw will lead to component failure by a future time. Plot 100,shown in FIG. 1, sketches a curve 101 representing the probability offailure within a time, Δt. A damage tolerance limit 103 is selectedbased on an acceptable probability of failure 105.

Because failure is probabilistic, inspections are traditionallyscheduled periodically so that a flaw can be detected early in itsgrowth cycle, well before it is likely to develop to the point ofcausing component failure. Different inspection technologies will becapable of detecting flaws at different points in their growth cycle andtherefore the inspection interval depends upon the type of inspectionbeing performed and its expected detection performance at the locationof interest.

SUMMARY OF THE INVENTION

In accordance with an embodiment of the invention, there is provided acomputer-readable storage medium comprising computer-executableinstructions that, when executed by at least one processor, perform amethod comprising acts of: receiving at least two sets of sensor data,each of the at least two sets of sensor data comprising spatial data fora measured material condition of a component; spatially registering theat least two sets of sensor data with respect to each other and thecomponent; computing a change in the material condition of the componentfrom the spatially registered at least two sets of sensor data;estimating the current condition based at least in part on the change inthe material condition; and predicting a future condition of thecomponent at a future time based at least in part on the estimatedcurrent condition, the future condition of the component being predictedusing a database comprising a plurality of precomputed materialconditions of the component, each precomputed material conditioncomputed for a respective operating condition and time. The methodfurther comprises generating the precomputed material conditions using aflaw growth model; storing the precomputed material conditions in thedatabase; filtering at least one of the at least two sets of sensor datawith at least one flaw signature; and estimating a current condition ofthe component from the filtered sensor data, and a stored database ofhistorical sensor data from a simple element selected to represent thecomponent material and flaw growth behavior.

In further, related embodiments, each of a plurality of data points inthe database may be generated for a respective combination of anequivalent number of fatigue cycles and stress level. The storeddatabase may comprise at least one coupon test representative of thecomponent. Predicting the future condition of the component may compriseestimating a service loading experienced by the component based at leastin part on the change. The act of estimating the current condition maycomprise using the change in material properties and archived data, thearchived data relating flaw size to sensor signal data.

In another embodiment according to the invention, there is provided amethod of predicting a risk of failure before a future time. The methodcomprises inspecting a feature of a component using a non-destructivetesting (NDT) method, wherein the NDT method is performed at a pluralityof inspection times at a plurality of locations on the component, theNDT method producing inspection data for the plurality of locations ateach of the plurality of inspection times; storing the inspection datain a computer-readable storage medium; operating at least one processorto determine, based at least in part on the inspection data, if a damagefeature is growing within the component and, when insufficientinformation exists to reliably detect the damage feature using theinspection data at one of the inspection times, generating an enhancedresponse from the inspection data at two or more of the inspection timesand using a precomputed database with two or more dimensions as afunction of sensed condition and usage that is searched to determine therisk of failure before the future time.

In further, related embodiments, the enhanced response may be a functionderived from sensor data at a same location on the component for each ofthe two or more inspection times. Data at other locations may also beused to formulate the function to generate enhanced response. Asignature library may be used to derive the enhanced response. The NDTmethod may be an eddy current array. The plurality of locations maycomprise a fatigue critical location on the component, and usage may bemeasured in equivalent fatigue cycles, and the database may be generatedusing a damage evolution model. The plurality of inspection times maycomprise a first and second time, the first time being a time before thecomponent is put into service and the second time being a time after thecomponent is put in service, and the inspection data may comprise firstinspection data taken at the first time and second inspection data takenat the second time. The flaw may be a crack in the component and it maybe determined that insufficient information exists to reliably detectthe crack using the inspection data at one of the plurality ofinspection times if a probability of detecting the crack is below athreshold. The threshold may be about 90 percent probability ofdetection, and failure may comprise a size of the crack reaching acritical crack size.

In another embodiment according to the invention, there is provided amethod of predicting a future time at which a critical damage level willbe reached. The method comprises inspecting a feature of a componentusing a non-destructive testing (NDT) method, wherein the NDT method isperformed at a plurality of inspection times at a plurality of locationsof the component, the NDT method producing inspection data for theplurality of locations at each of the plurality of inspection times;storing the inspection data in a computer-readable storage medium;operating at least one processor to determine, based at least in part onthe inspection data, if a damage feature is growing within the componentand, when insufficient information exists to reliably detect the damagefeature using the inspection data at one of the plurality of inspectiontimes, to generate an enhanced response from the inspection data at twoor more of the plurality of inspection times and using a databasegenerated using a model of damage evolution to predict the probabilitydistribution of future times at which the critical damage level will bereached.

In further, related embodiments, the future time may be measured inequivalent fatigue cycles, the damage level may be crack size, thecritical damage level may be a critical crack size, and the location ofinterest on the component may be a fatigue critical location.

In another embodiment according to the invention, there is provided amethod for tracking process progression comprising operating a processorto: process a first inspection image of a component to rank an originalplurality of locations of the component, wherein the original pluralityof locations are ranked based on a quantitative measure that correlateswith predicted crack growth rate at the respective location; filter asecond inspection image of the component using filters devised fromsignatures to suppress indications that are not representative of acondition of interest and enhance the response of conditions that aremore likely to represent the condition of interest; and re-rank theoriginal plurality of locations using the filtered second inspectionimage including additional highly ranked locations, wherein the secondinspection image is acquired at a later time than the first inspectionimage.

In further, related embodiments, the method may further compriseextracting the signatures from a representative fatigue test article;and storing the signatures in a signature library on a computer-readablestorage medium. The quantitative measure may be a peak conductivity atthe respective location. The quantitative measure may be a half-heightwidth of conductivity dip at the respective location. The quantitativemeasure may be a peak filter response at the respective location. Afatigue progression track may be identified based on a statisticallysignificant trend in non-destructive test (NDT) data from two or moreinspection times, where the top ranked location is maintained for eachinspection until the end of the component's useful life. Multiple NDTpasses may be recorded at each inspection time.

In another embodiment according to the invention, there is provided acomputer-readable storage medium comprising computer-executableinstructions that, when executed by at least one processor, perform amethod comprising acts of: spatially registering a baseline response ofa component and a current response of the component; after the spatiallyregistering, subtracting the baseline response from the currentresponse; and estimating a probability distribution of a currentcondition of the component by applying a statistical analysis using aset of responses from one or more simplified elements.

In further related embodiments, the baseline response may be a digitalnon-destructive test (NDT) image from an inspection performed prior todeployment of the component, and the current response may be a digitalNDT image from an inspection performed after deployment and during aservice life of the component. Estimating the probability distributionof the current condition of the component may comprise estimating aprobability density function.

The foregoing is a non-limiting summary of the invention, which isdefined by the attached claims.

BRIEF DESCRIPTION OF DRAWINGS

The accompanying drawings are not intended to be drawn to scale. In thedrawings, each identical or nearly identical component that isillustrated in various figures is represented by a like numeral. Forpurposes of clarity, not every component may be labeled in everydrawing. In the drawings:

FIG. 1 is a plot sketching the probability of failure within a time Δtgiven a current damage level of a component;

FIG. 2 is a block diagram of an inspection system according to someembodiments;

FIG. 3 is a block diagram of a system for distributing hyperlattices toinspection systems according to some embodiments;

FIG. 4A is a plot illustrating at least a portion of a hyperlatticeaccording to some embodiments;

FIG. 4B is a plot showing predicting flaw growth in a component underdifferent operating conditions;

FIGS. 5A-5B is a flow diagram of a method for adaptively managing thelife of a component according to some embodiments;

FIG. 6A is an example presentation of inspection data according to someembodiments;

FIG. 6B is a example presentation of indications identified frominspection data according to some embodiments;

FIG. 6C is an example user interface for receiving input from anoperator that indicates further actions to be performed for a set ofindications;

FIG. 6D is a sketch of a component with markers for facilitating spatialregistration of multiple sets of inspection data imaged from thecomponent;

FIG. 6E is an illustration of an alignment process for two sets ofinspection data that utilizes the images of markers on the inspectedcomponent;

FIG. 7A is a data plot of conductivity data obtained from a titaniumalloy sample after 15,000 and 21,000 stress cycles;

FIG. 7B is a data plot of change in conductivity after baselining the21,000 stress cycle data with the 15,000 stress cycle data;

FIG. 8A is a sketch illustrating metrics for characterizing a flawdetection;

FIG. 8B is an example plot of the measured response to a flaw (â) versusthe actual size of the flaw (a);

FIG. 9A shows a set of plots illustrating probability distributions forinputs into a hyperlattice;

FIG. 9B is a block diagram illustrating operation of a prediction moduleaccording to some embodiments;

FIG. 9C is an example cumulative distribution function output from aprediction module;

FIG. 10A is a sketch of a representation of a portion of a hyperlatticespace according to some embodiments;

FIG. 10B is a sketch illustrating a representation of the risk offailure according to some embodiments; and

FIG. 11 is a flow diagram of a method for adaptively managing the lifeof a component according to some embodiments.

FIG. 12A-12Z show a graphical user interface for controlling adaptivelife management according to some embodiments; and

FIG. 13A-13J show a graphical user interface for controlling adaptivelife management according to some embodiments.

DETAILED DESCRIPTION OF THE INVENTION

A framework is provided for adaptively managing the life of components.The framework provides a system for accurately predicting componentlife, scheduling component inspections, and a decision making processfor maintaining and replacing components. The inventors have recognizedand appreciated that remaining component life is inherentlyprobabilistic and that using information collected in a sequence ofinspections may significantly improve estimates of components life,improve scheduling of inspections, and improve the decision makingprocess for performing conditions based maintenance (CBM) actions.

As used herein a “component” is any type of physical part or device. Insome embodiments, a component may be a constituent of a device. Though,a device, regardless of its number of constituent parts, may be acomponent. Examples of types of components include rotorcraftcomponents, fixed wing aircraft components, drill pipe connections, oilpipelines, composite skins, and medical implants. In some embodiments acomponent is a part of an aircraft, such as an airplane, glider, orhelicopter, or UAV. Though, it should be appreciated that the frameworkmay be used with components of any suitable type.

Components may be made out of any suitable material or combination ofmaterials. For example and not limitation, component may be made ofmaterials such as metals, alloys, ceramics, asphalts, transparencies,rubber, glass, cable bundles, composites, and matrix/fiber materialssuch as carbon fiber reinforced composites. Some components may be madeup of a combination of materials. For example, a component may includeseveral material layers. The layers may include different materials andmay feature materials of the same type but at different orientationswith respect to one another. For example, a component made from a fiberbased composite may include a stack up of multiple layers with the sameor differing orientations of the fibers. Practitioners may refer to acomponent as a “critical component” if in-service failure of thecomponent is unacceptable.

Components may be shaped or used in such a way as to have one or morefeatures at which the fatiguing effects of the operating conditions aremore significant than other locations on the component. As such, growthof flaws to a critical size at any of these locations may represent thelikely failure modes for the component. Practitioners may refer to thesefeatures as “hot spots,” “control points,” or “fatigue criticallocations.” Some examples of hot spots may include bolt hole locations,connection points, narrow regions, and other features of the componentthat tend to be subject to increased damage rates, such as from higherstresses under the component's operating conditions.

During operation a component's condition may deteriorate due to thedevelopment and growth of flaws in the material of the component, suchas the growth of a crack or the development of deleterious conditionsuch as residual stress relaxation. Deterioration of the componentscondition may result from the material of the component having a lowerresidual strength. Such damage to the component may develop near thecomponent's hot spots. Though, it should be appreciated that flaws maydevelop anywhere on a component. For example, some flaws may begenerated by impact damage. While the presence of flaws may foreshadowthe onset of reduced functionality or failure of the component, actualreduction in functionality of a component is not required for a flaw tobe present as many components are “over designed” to accommodate damagewithout any reduction in performance. What constitutes damage depends onthe function and material of the component, more particularly on thefunction of the component for which in-service component failure is tobe avoided. Examples of damage for components providing mechanicalstrength made of metals and alloys include metal fatigue, cracks,corrosion, thermal, thermomechanical, and mechanical impact damage. Asanother example, damage of components providing mechanical strength madeof matrix/fiber composites include cracks, impact damage to the matrixand fibers, thermal damage, fatigue, machining effects such as cuttingand drilling, damage from mechanical and thermal overloads, andenvironmental damage such as corrosion.

Adaptive life management may be performed for a single component or agroup of components. A group of components of the same type that arebeing monitored are herein referred to as a pool. A component lifemanagement system may perform life management for more than one type ofcomponent.

Component lifetime may be measured in equivalent fatigue cycles. Cyclesmay be defined in any suitable way such as to allow a consistentcomparison between, for example, different time periods or differentcomponents. Examples of definitions for counting cycles includeground-air-ground (GAG) cycles, and total accumulated cycles (TACs). Insome embodiments, cycles may be measured as equivalent usage hours underprescribed operating conditions. It should be appreciated that, unlessotherwise stated, use of the word time refers to a chronologicalprogression that may be measured in seconds, equivalent cycles, cycles,or any other measure of chronology in a process.

The risk of failure of a component is the probability of having a flawgrow beyond a critical flaw size. The critical flaw size may, forexample, be the flaw size at which the flaw growth rate will increase toa point that will cause failure in the next service period (that isbefore the next inspection opportunity). Note that the critical flawsize may vary for different features of the component. For example,failure for a crack may be defined as a point at which the crack sizereaches a prescribed crack depth within a predefined set of locations atone or more critical features on a critical component. In someembodiments, laboratory tests may be performed to define the criticalflaw size. Though, it should be appreciated that the critical flaw sizemay be defined in any suitable way.

FIG. 2 is a block diagram of an inspection system 200 according to someembodiments. Inspection system 200 includes a component inspectionmodule 220 and a computing system 240.

Component inspection module 220 obtains inspection data by inspecting acomponent 260 and provides this inspection data to computing system 240.In some embodiments, component inspection module 220 includes sensorsfor performing a non-destructive test (NDT) of component 260. Thesensors may provide good repeatability from scan to scan such thatcomparison between inspection data taken at different cycles ispractical. In some embodiments, component inspection module 220 may usean electromagnetic based sensing technology, an ultrasonic based sensingtechnology, or any other suitable sensing technology or combination oftechnologies. For example an eddy current sensor, such as a meanderingwinding magnetometer (MWM) sensor, may be used to inspect components. Asanother example a capacitance sensor, such as a dielectrometry sensor,may be used to inspect the component.

In some embodiments, component inspection module 220 provides a highresolution imaging of a component in, for example, one, two, or threespatial dimensions. NDT inspections may produce a one, two, or higherdimension record/image that relates to the material condition over asurface or volume of a component or other material configuration. Theinspection data may be digitized for storage in a computer-readablestorage medium. NDT inspection methods that produce digital data may bereferred to as “digital NDT”. The sensor may image some measure ofdamage or some property of the material that is related to damage suchas the microstructure or micromechanical features of the component'smaterial. In some embodiments one or more electrical properties of thecomponent's material are imaged by the component inspection module 220.The measured electrical properties may be related to damage features.

Components 260 may be one or more components that are being inspected.Components 260 may be any suitable type of component, may be a pool ofcomponents of the same type, or multiple pools of components. In someembodiments, components 260 are components of a fleet of aircraft.

Computing system 240 may be any suitable type of computer configured toreceive and process sensor data from component measurements. In someembodiments, computing system 240 comprises a plurality of computers.The computers may be operably connected via any suitable networkingtechnology. In some embodiments, inspection module 220 and a computingsystem 240 are integrated into a single unit, for example, a handhelddevice. In some embodiments, inspection module 220 and a computingsystem 240 may be separate units. Though, inspection module 220 and acomputing system 240 may be provided in any suitable way.

Computing system 240 has a processor 241 operably connected to a memory242. Processor 241 may be any suitable processing device such as, forexample and not limitation, a central processing unit (CPU), digitalsignal processor (DSP), controller, addressable controller, general orspecial purpose microprocessor, microcontroller, addressablemicroprocessor, programmable processor, programmable controller,dedicated processor, dedicated controller, or any other suitableprocessing device. In some embodiments processor 241 comprises one ormore processors. For example, processor 241 may have multiple coresand/or be comprised of multiple microchips.

Memory 242 may be integrated into processor 241 and/or may include“off-chip” memory that may be accessible to processor 241, for example,via a memory bus (not shown). Memory 242 may store software modules thatwhen executed by processor 241 perform a desired function. Memory 242may be any suitable type of computer-readable storage medium such as,for example and not limitation, RAM, a nanotechnology-based memory, oneor more floppy discs, compact discs, optical discs, volatile andnon-volatile memory devices, magnetic tapes, flash memories, hard diskdrive, circuit configurations in Field Programmable Gate Arrays, orother semiconductor devices, or other tangible, non-transient computerstorage medium.

Computing system 240 also includes suitable input/output (I/O) 243. I/O243 comprises any suitable hardware and software for interacting withcomputing system 240. For example, I/O 243 may include a user I/O 252and a network interface 253.

Network interface 253 may be any suitable combination of hardware andsoftware configured to communicate over a network. For example, networkinterface 253 may be implemented as a network interface driver and anetwork interface card (NIC). The network interface driver may beconfigured to receive instructions from other components of computingsystem 240 to perform operations with the NIC. The NIC provides a wiredand/or wireless connection to the network. The NIC is configured togenerate and receive signals for communication over network. In someembodiments, computing system 240 is distributed among a plurality ofnetworked computing devices. Each computer may have a network interfacefor communicating with other the other computing devices formingcomputing system 240.

Computing system 240 may include one or more databases such as signaturelibrary 244, condition progression database 245, and inspection archive251. The databases may be stored in memory 242, though this is just anillustrative embodiment and other storage locations are possible.

Signature library 244 is a library of sensor responses for componentflaws. Signatures may be generated from experiment, analytical models,computer simulation, any suitable combination thereof, or in anysuitable way.

In some embodiments, a study is performed on simple elements and/orrepresentative fatigue test articles to generate crack signatures.Simple elements or simplified elements are elements, coupons orotherwise representative configurations of a material of interest.Simple elements may be processed (e.g. fatigue tested, heat treated,shot peened, machined) in a manner representative of the behavior ofinterest and NDT data is recorded on the simple elements at differenttimes or stages within the process at prescribed locations within thematerial volume. A representative fatigue test article may be a simpleelement or a more complex element that represents a fatigue criticallocation on a component.

A suitable coupon may be made of the same material as the component tobe inspected. Baseline sensor measurements of the coupon may be taken,for example, before a crack develops. The coupon may then be fatigued byan applied cyclic load. The coupon may be scanned periodically using theinspection sensor as a crack develops. A secondary measurement techniquemay be used to characterize the crack such that the resulting scan maybe identified with the “actual” crack characteristics. In someembodiments, acetate replicas or fractography may be used. Theinspection sensor data is used to locate cracks in the replicas forlarger crack sizes so the earlier replicas can be used to locate thecracks before sufficient sensor signal-to-noise existed for reliabledetection.

The secondary measurement technique may provide a direct measurement ofthe flaw size. Though any suitable measurement technique may be used.The secondary measurement technique may be another non-destructivetesting technique. Though, in some embodiments a destructive measurementtechnique is used. It should be appreciated that the secondary testingtechnique may not be suitable for field measurements of the component.This may be due, for example, to the time it takes and/or the cost ofperforming the secondary measurement.

In some embodiments the flaw signatures are filtered. For example, theflaw signatures may be baseline subtracted. That is, the sensor responseto the coupon prior to development of the flaw may be subtracted fromthe sensor response to the coupon after development of the flaw. Theflaw characteristics may be known with high accuracy by using secondarymeasurement techniques. In another embodiment, a selected signature fromthe signature library may be used to construct a digital filter toenhance the flaw response and suppress noise.

Computing system 240 may also include inspection archive 251. Inspectionarchive 251 may store information related to previous component tests,inspection schedules for the components, history of condition basedmaintenance actions, predicted operating conditions for the component,and any other suitable information related to a component, pool orfleet. In some embodiments, inspection archive 251 maintains informationfor a number of the same type of component. For example, information maybe stored for each component in a pool. Inspection archive 251 may alsostore statistics generated for a pool and information for differenttypes of components.

Condition progression database 245 stores the execution results forinputs to a condition progression model, which is also referred to as aphenomenological model. The execution results may be tabulated bycondition progression database 245 in the form of a hyperlattice. Ahyperlattice is an n dimensional nonlinear parameter space generatedfrom a phenomenological model for the growth of component flaws. Here nmay be a counting number (1, 2, 3, . . . ). In the special cases of n=2and n=3 the hyperlattice is referred to as a grid and a lattice,respectively. The hyperlattice may be used as a look-up table. Thephenomenological model and the generation of a hyperlattice isdiscussed, for example, in connection with FIG. 3, below. In someembodiments, condition progression database 245 may store more than onehyperlattice. Multiple hyperlattices may be stored when different rangesand/or densities of input parameters are used to generate thehyperlattices. Also, hyperlattices may be generated by different modelsif different types of flaws may be present in a component. For example,different crack morphologies may have different hyperlattices.

In some embodiments, a hyperlattice is a database that is computed usinga phenomenological model where one dimension of the hyperlattice ismaterial condition and another dimension of the hyperlattice is ameasure of time (e.g., cycles or some chronology). The materialcondition and measure of time may be measurable, using a sensor or othermeans, within some finite uncertainty. The hyperlattice may alsoincludes at least two additional properties selected for estimation. Inone embodiment, the two unknown properties are remaining life andstress. In another embodiment, the properties are crack size and stresswhere the crack size unknown to be estimated is the same as thatmeasured by the sensor. When the unknown is remaining life, theremaining life may be defined as the time remaining to reach a criticalcrack size, where the critical crack size may vary with the estimated orpredicted applied stress.

A lattice point is a data point in the hyperlattice database. In someembodiments, a lattice point may include at least four values, forexample, two measured values and two values of parameters to beestimated. The values of the parameters to be estimated may be generatedoffline using the phenomenological model for the range of possiblevalues for the two estimated unknowns over the range of the possiblevalues of measured values.

Plot 410, shown in FIG. 4A, shows an example of at least a portion of ahyperlattice along with some exemplary data to illustrate some aspectsof use of the hyperlattice according to some embodiments. In thisexample, the material condition is crack length which is plotted on axis411. Time is measured in cycles and is plotted on axis 413. A grid 420is plotted on plot 410. The parameters estimated by grid 420 areremaining life and stress. Arrow 421 indicates the direction ofincreasing stress and arrow 423 indicates the direction of increasingremaining life. The crack length may be estimated at inspection time t1using sensor data. Here the sensor data is characterized by a metric415, â₁. A probability distribution 416 of crack lengths is estimatedfrom â₁. A probability distribution 425 estimates the number of cyclesthe cracked component was in service at inspection time t1. Region 428in the grid represents regime of likely stresses and remaining lifegiven probability distribution 416 of crack length and probabilitydistribution 425 of number of cycles. A second inspection is also shownat time t2. Metric 417, â₂, characterizes the sensor response at timet2. A probability distribution 418 of crack lengths is estimated fromâ₂. A distribution function for the number of cycles may also beestimated for t2 (not shown). From the probability distributions for thecrack lengths and the number of cycles at t2 the stress and remaininglife of the component may be estimated. The estimated stress andremaining life are represented by probability distribution 427 and 426,respectively. From the lattice it can be seen that the locus of criticalcrack sizes 422 (remaining life is 0%) predicted from the hyperlatticeis at around 100 mils.

Computing system 240 may include computer executable software modules,each containing computer executable instructions. The software modulesmay be stored in memory 242 and executed by processor 241, though thisis just an illustrative embodiment and other storage locations andexecution means are possible. In some embodiments, receiving module 246,filtering module 247, estimation module 248, prediction module 249,decision module 250 and reporting module 254 may be implemented ascomputer executable modules. However, these modules may be implementedusing any suitable combination of hardware and/or software.

Receiving module 246 is configured to receive inspection data fromcomponent inspection module 220. In some embodiments, receiving module246 interfaces with component inspection module 220 through a wired orwireless interface. For example, component inspection module 220 may beconnected to computing system 240 via a USB, IEEE 1394 connection,through an Ethernet, Bluetooth or IEEE 802.11 network. In someembodiments, a computer-readable storage medium, such as a compact flashdisk is used. Though, inspection data may be provided to computer system240 in any suitable way.

Once the inspection data is received by receiving module 246 the datamay be passed to filtering module 247 for filtering. In someembodiments, receiving module 246 stores the inspection data ininspection archive 251.

Filtering module 247 may filter the inspection data to enhance theobservability of component conditions of interest and to suppressindications that are not of interest. In some embodiments, filteringmodule 247 performs baseline subtraction. Baseline subtraction may beperformed by spatially registering earlier inspection data with thepresent inspection data and taking the difference. Earlier inspectiondata may be obtained, for example, from inspection archive 251.Filtering module 247 may also filter the inspection data usingsignatures from signature library 244.

Estimation module 248 may estimate the current condition of thecomponent. The current condition may be estimated using previousinspection data, hyperlattice look-ups, or in any suitable way. In someembodiments, the current condition is described probabilistically, forexample, by a probability distribution function or a cumulativedistribution function. In some embodiments, the distribution function isa Gaussian distribution defined by a mean and standard deviation.

To estimate the current condition estimation module 248 may identify thelocation of flaws on the component. Flaw sites will promote damageevolution at a faster rate than locations without such damage. Theconstellation of flaws and their respective types and sizes may berecorded and stored in inspection archive 251. Identifying current flawsmay be facilitated in part by flaws that were identified on thecomponent as part of a previous inspection. The location of flaws may bemapped and the evolution of the flaws tracked across inspections. Theflaws may be ranked, for example, based on the risk of component failurethey present.

Prediction module 249 predicts the future condition of the component ata future time. In some embodiments, prediction module 249 performs alook-up and interpolation in condition progression database 245 topredict the future condition or time. The prediction model may beconfigured to select an appropriate hyperlattice from conditionprogression database 245. Selection of the hyperlattice may be based forexample, on expert input, the current condition, previous flawdetections, expected flaw growth.

Prediction module 249 may include a rapid, multivariate, nonlinearsearch tool. The search tool may generate real time estimates of unknownproperties of the condition of a component and the uncertaintydistribution for those properties.

The flaw sites, types, and sizes may stored by evaluation module 248 ininspection archive 251 may be input to the hyperlattice or thephenomenological models for identifying and bounding the time that newdamage sites appear on a component such as a metal dynamic rotorcraftcomponent, or a composite wing skin or propeller blade or on an oilpipeline.

After the future condition and/or future time have been predicted,decision module 250 may determine what action, if any, should bescheduled or made for the component. In one such embodiment, if themechanical/impact damage level is below a threshold that enables it toremain in service (even though it was detected and documented by thesensing method) then it is valuable to map and track these sites, and torecord the time at which they appeared. Then the damage evolution can bemonitored for each site to assess risk, and the possible interaction ofsites that are close enough to increase risk of failure, can beincorporated into models. Decision module 250 may schedule a nextinspection of component, determine that the component should bereplaced, and/or determine that the component should be repaired.Inspections may be scheduled at equal intervals or spaced in sequencesthat improve flaw growth rate (derivative) estimation or in any otherpattern that improves estimation or prediction of component conditions.

Condition progression database 245 may be periodically updated toreflect additional knowledge obtained through the course of managing apool of components. The underlying models on which the hyperlattices aregenerated may be adjusted, for example, to correct estimated parametersand assumptions that are better understood. In some embodiments, asystem 300, shown in FIG. 3, is used to distribute condition progressiondatabase 245. In some other embodiments, computer system 240 may includemodels for generating the hyperlattices for condition progressiondatabase 245 (FIG. 2).

A reporting module 254 may be configured to generate reports documentingthe inspection, detection of flaws, estimated conditions and predictedconditions, the action to be taken for the component, and the like.Reporting module 254 may populate a database that may be accessed byadministrators and experts. In some embodiments, the database may beaccessed over a network. In some embodiments, reporting module 254generates a word processor document report. The report may be printedout or stored on a computer, for example, in association with thecomponent.

As shown in FIG. 3, server 300 may be connected to one or moreinspection systems 200 (see also FIG. 2) via a network 310. An updatedversion of condition progression database 245 may be downloaded fromserver 340 to the respective inspection systems 200. In someembodiments, only some hyperlattices stored in condition progressiondatabase 245 of server 300 may be downloaded to particular inspectionsystems. The availability of hyperlattices may be determined, forexample, based on licensing arrangements.

In some embodiments, inspection systems 200 may also upload inspectiondata, statistics, component conditions, and the like to server 340.Server 340 may have a processor 341, memory 342 and I/O 343 similar tothose described for processor 241, memory 242, and I/O 243 above (seeFIG. 2).

Hyperlattices stored in condition progression database 245 may begenerated by a condition progression module 344 which provides aphenomenological model for predicting the evolution of component damageor anticipating kinematic, static, dynamic environmental or materialchanges in the component. The flaw growth rate predicted by the modelmay depend on the operating conditions incurred during each cycle by thecomponent. Different operating conditions may result in different timeperiod for growing a flaw to its critical size. Plot 400, shown in FIG.4B, is a sketch of two different flaw growth curves for two differentoperating conditions. Specifically, plot 400 illustrates the growth inflaw size (axis 401) as a function of the number of operating cycles(axis 402). Curve 403 is a flaw growth curve for stress σ₀ and curve 404is a flaw growth curve for stress σ₁. Both curves assume the sameinitial condition for the component. As sketched, σ₀>σ₁. Also marked inplot 400 are the detectable flaw size 405 and the critical flaw size406. The detectable flaw size is a flaw that can be detected with adefined probability of detection (POD) with a defined probability offalse alarm (PFA). The POD and PFA of the detectable flaw size may, forexample, be specified to suitable levels for a specific application.

The phenomenological model may predict component conditions such as howflaw size affects the sensor response, property (such as effectiveelectrical conductivity or magnetic permeability) variations with impactdamage, thermal changes in electrical properties, dielectric constantchanges with thermal exposure, and any other suitable property of thecomponent and how the property affects sensor response. The model may becomponent specific, and may be tailored for the materials used toconstruct the component.

The phenomenological model may be physics based (e.g., fracturemechanics model, fatigue model), system dynamics based, parametric,logic based, empirical study based, or based on field and productionexperience, or any suitable combination thereof. Though, any suitabletype of phenomenological model may be used. In some embodiments,different phenomenological models are used to model the evolution ofdifferent types of flaws. A crack, for example, may have severaldifferent morphologies. A cracks may develop as long and shallowdiscrete crack, a cluster of similarly sized microcracks, or a clusterof variable sized small cracks with one larger crack. The evolution ofthese crack morphologies may be modeled using different phenomenologicalmodels and accordingly, different hyperlattices may be produced. Themodels may also account for the proximity of damage sites on a componentas flaws located sufficiently near one another may have a differentdamage progression path than in isolation. In some embodiments, thephenomenological models may be provided and modified by one or moreexperts in the relevant technical arts.

The phenomenological model may be used to generate a hyperlattice ofconditions of the component. The input conditions used to generate thehyperlattice from the model may be derived from laboratory studies ofthe component's material, knowledge from experts such as originalequipment manufacturers (OEMs). For example, input conditions may bedetermined from coupon studies of crack initiation and growth in arepresentative environment. Though, any suitable source may be used todetermine the inputs for the phenomenological model.

The phenomenological model and resulting hyperlattices may be calibratedto improve their predictive power by using reference part calibration orstandardization techniques. In some embodiments, server 300 may providethe uploaded information collected from inspection systems 200 to theexperts as feedback for actual component damage evolution. Also, retiredcomponent may fatigued to actual failure while collecting fatiguerelated data. Such a test may be used to determine the actual remaininglife of a component. In some embodiments, a retired component mayundergo secondary testing (destructive or non-destructive) to determinethe actual condition of the component at retirement. This informationmay be used to reconfigure the phenomenological models to better agreewith historical data, generate improved hyperlattices, provide improveduncertainty estimates, usage estimates, initial flaw size estimates,inclusion density, grain decohesion propensity, surface roughness,residual stress, mechanical damage conditions, and the like.

In some embodiments certain model parameters may be modified to producemodel outputs that agree with reference part calibration data, fleetsensor measurements, values based on expert knowledge, or theprobability distribution of sensor measurements for a similar component.The parameters may represent, for example, the material condition suchas residual stress distribution, assumed inclusion density and assumedinitial crack size distribution. Though, the parameters may representany suitable variable. In some embodiments, the reference partcalibration data represents the condition of a component after a knownnumber of cycles and given stress level. Accordingly, the initialassumptions about the material at completion of manufacturing (i.e., at0 cycles) may be adjusted such that the phenomenological model predictsthe condition of the reference part at the known number of cycles forthe given stress level. As a specific example, the assumed distributionfunction (e.g., maximum likelihood value and uncertainty) of the initialinclusion size may be adjusted to match the distribution function of thecondition of a pool of coupons or components at the given time in thefuture and for a given stress level. Though, other sources of thedistribution function may be used as well. For example, expert knowledgemay be used to estimate distribution functions for a defined number ofcycles and given stress level. Uncertainty may be selected withconstructive and destructive cumulative uncertainty from multiplesources such as model input, operation conditions, sensor error, groundtruth errors in calibration data, recalibration data, and populationdata.

In some embodiments, the hyperlattice is assumed fixed and theinspection sensor responses, usage and other measured data arecalibrated to match the hyperlattice. In the case where the hyperlatticeis assumed fixed, inspection data may be taken using the componentinspection module on components or samples with known properties. Atransformation is applied to the inspection data such that thetransformed inspection data is in agreement with the hyperlattice. Insome embodiments, a transformation may include an adjustment to theeffective cycles to match the reference calibration data to thehyperlattice. In some embodiments, flaw size estimation filters areadjusted as part of the transformation to match hyperlattice predictionsand other ground truth data. The determined transformation may then beapplied to inspection data that is taken on samples with unknownproperties for other estimation and prediction computations. Furtheraspects of this calibration technique may be found in ASTM-E2338.

Server 300 may also include an expert management module 350 for managingthe experts that define the phenomenological models of conditionprogression module 344. For example, module 350 may provide a tool forenabling a team of experts to work together to refine thephenomenological models. In some embodiments, expert management module350 provides a web based interface and/or portable device for experts toaccess inspection data, coupon data, the current phenomenologicalmodels, hyperlattices, and any other information relevant to definingthe phenomenological models or assessing its performance. Expertmanagement module 350 may limit information access to individual expertsaccording to their respective access rights. Some experts may be given asupervisory role to control versions of the phenomenological models andscrutinize the work of other experts to ensure the reliability of thephenomenological models and the hyperlattices generated therefrom.

Method 500, shown in FIGS. 5A-5B, is a method of adaptively managing thelife of a component. Method 500 may be implemented in any suitablecombination of hardware and software. For example, method 500 may beimplemented in inspection system 200. In some embodiments, steps ofmethod 500 are stored as instructions on a computer-readable storagemedium. When the instructions are executed, the corresponding methodstep maybe performed. In some embodiments, a graphical user interfacemay guide an operator through performance of various steps in themethod.

It should be appreciated that the steps of method 500 may be performedin any suitable order and FIGS. 5A-5B merely illustrate method 500according to some embodiments. It should also be appreciated that insome embodiments some steps of method 500 may be optional.

At step 501, initial inspection data is taken for a component. Thisinitial data may be taken prior to putting the component into service.For example, the initial inspection may be done at the end of themanufacturing process. Inspection may be performed for the entire partor may be limited to a set of locations such as hot spots representativeof the most probable failure modes for the component.

In some embodiments, inspection data is collected during manufacturingas well. For example, the component may be inspected before and aftercertain manufacturing steps. A component may be scanned before andafter, heat treating, surface treatments (e.g., shot peening) and thelike. In some embodiments, the same inspection technique is performedmultiple times. By taking multiple measurements at each point,instrument and setup noise may be suppressed by averaging. In someembodiments, inspection data may be taken in multiple orientations. Forexample, a component made of a material with anisotropic conductivitymay be scanned in multiple directions with a MWM-Array sensor todetermine the conductivity in different directions.

Plot 630, shown in FIG. 6A, illustrates an example of inspection data ona component. In this example, the inspection sensor is an MWM-Arraysensor, and the surface conductivity is the material property beingplotted in grayscale. Axis 631 and 633 may give the physical dimensionsin the respective directions such that the conductivity data may beassociated with a particular point on the component. Scale 635 shows theconductivity scale. In some embodiments, the scan results are presentedto the operator and the operator may confirm the inspection.

In some embodiments, metadata is provided for the component beinginspected at step 501. The metadata may contain information such as thetype of component, a serial number for the component, identification ofa device the component is part of (if any), the type of material thecomponent is made of, the sensor being used to obtain inspection data,the material of the component, any special treatments performed to thecomponent such as surface treatments, any previous condition basedmaintenance actions performed on the component, information about theoperator, information about the conditions of the measurement such asdate, time, temperature and humidity, risk tolerance levels, and anyother suitable information. The metadata may be used in the performanceof method 500.

At step 503, it is determined whether the component is acceptable to beput into service. The determination may be based, for example, on theinitial inspection data collected at step 501. In some embodiments, theinitial inspection data is processed to identify areas of possibleconcern. For example, if the inspection data indicates surfaceconductivity, a local drop in conductivity may be indicative of apotential crack in the material at that location. Indications may beranked based on the likelihood that they represent a flaw in thecomponent. The indications may be presented to an operator for review.Plot 637, shown in FIG. 6B, shows an example of how indications may berepresented for a component. In this example the top five rankedindications 638 are shown. However, any suitable number of indicationsmay be ranked and presented. Legend 639 presents the ranking. Here, zerorepresents the unranked space of the component. Axis 631 and 633 providereference to position on the component for plot 637.

In some embodiments, the operator is given the option to determine howthe indication should be treated. For example, the operator may rejectthe component based on the indication, may indicate that the indicationis not actually a flaw, or may indicate that the indication should betracked in future inspections. In some embodiments, the operator mayprovide a comment regarding the decision. The comment may be stored, forexample, in metadata along with the inspection data. Window 640, shownin FIG. 6C, illustrates an example user interface for the operator.Window 640 shows the top indications 641, their position 642, and theirsensor response 643, â (“a hat”). (Determining the sensor response isdiscussed, for example, in connection with step 517, below.) A statusfield 644 allows the operator to select a status for the indication(e.g., reject component, track indication, ignore indication).Additionally a comment field 645 may be used by the operator to inputinformation about the selection. Once the operator is satisfied,“Validate” button 646 may be selected.

If the component is rejected at step 503, method 500 ends. If thecomponent is accepted at step 503, method 500 continues to step 505.

At step 505, the next inspection time is set. The inspection time may bean actual time or may be a number of cycles. The next inspection timemay be determined based on the initial inspection data, fatigue testsperformed on coupons and representative components, expected operatingconditions for the component once it enters service, damage evolutionmodels for the component. In some embodiments, the next inspection timeis set by assuming the largest undetectable flaw and using the damageevolution model to predict a time when the flaw has progressed to acertain level (e.g., 20% of critical flaw size). The next inspectiontime may be set as the predicted time. Confidence in the initialcondition may also affect selection of the next inspection time. In someembodiments the next inspection time is chosen as a range. This providessome flexibility as to when the inspection may take place. This may beuseful, for example, when the component and component inspection moduleare only periodically collocated. For example, a component inspectionmodule may be located at an airbase where an aircraft lands. In anotherembodiment, a pair of future inspection times (or cycles) are selectedto improve observability of flaw growth rates.

In some embodiments, inspection after a certain number of cycles may bedesired, however, it may not be practical, or possible measure cyclesdirectly. Accordingly, an actual time may be chosen for inspection basedon a prediction of when the desired number of cycles will be reached.

In one embodiment, at step 507, the component is put into service. Oncethe component is in service it is periodically inspected in accordancewith steps 509-525. As shown in the flow diagram of method 500, thesesteps form a loop that are repeated until it is determined to retire thecomponent.

At step 509, it is determined whether it is time for the nextinspection. When the next inspection time is easily countable such asfor an actual time or a number of GAG cycles step 509 may be determineddirectly. In some embodiments, it is determined that it is time for thenext inspection only if the actual number of cycles is within aninspection range and the component and component inspection module arecollocated. Of course, if inspection is an actual time (e.g., Jun. 5,2009) it may be determined that the time for inspection is at that date.Step 509 loops until it is determined that it is time to inspect thecomponent. The time between inspections is not necessarily equal. It maybe set, for example, based on risk of failure before the nextinspection.

At step 511, the component is again inspected. Inspection may beperformed in ways similar to those described in connection with step501. The inspection may be performed using a component inspection modulesuch as component inspection module 220 (FIG. 2). As before multiplemeasurements at each location on the component may be taken to averageout noise. Inspection data may be presented, for example, in wayssimilar to plot 630 (FIG. 6A). Though, it should be appreciated thatinspection data may be presented in any suitable way.

At step 513, the inspection data obtained at step 511 is spatiallyregistered with inspection data obtained during a previous inspection.Spatially registering the inspection data aligns the inspection dataspatially so that the inspection data at the same location on thecomponent an be compared to one another between the two or moredifferent inspections. Spatial registration may also be made withreference to positions on the actual component so that the inspectionsdata can be understood with reference to the physical component.

In some embodiments, the component may have markers that have a uniquesignature when scanned by the component inspection module. FIG. 6D showsa component 600 with markers 610 and 620. The type of marker being usedmay depend on the inspection technology. For example, for a conductingpart on which inspection data is collected using an MWM array, markers610 and 620 may be marked using an insulating tape. The presence of theinsulating tape may produce a predictable response that will be presentin each measurement of the component. FIG. 6E shows inspection data 610and inspection data 620. Both sets of inspection data clearly imagemarkers 610 and 620. In inspection data 610, markers 601 and 602 appearas marks 611 and 612, respectively. In inspection data 620, markers 601and 602 appear as marks 621 and 622, respectively. The images arespatially registered by manipulating inspection data 620 such that marks621 and 622 are aligned with marks 611 and 612, respectively, ofinspection data 610. In another embodiment, markers may be existingpatterns in the sensor data or the edge of a part or another suchgeometric feature.

It is noted that the imaging of markers 610 and 620 may also be used tocorrect for lost position data. For example, in some embodiments asensor is scanned over the surface of a component. To correlate thesensor data with the physical location of the sensor a position encodermay be used. The position encoder may be, for example, an encoder wheelor an optical tracker (e.g., light emitting diode and photodiode). Ifthe position encoder seems inconsistent with the scan data such as whenthe encoder wheel jams or loses contact, the detected markers may beused to estimate the location of the sensor.

In some embodiments the markers have a shape that enables alignment inmultiple directions. Though, in some embodiments, alignment may beachieved by resolving the location of multiple markers.

At step 514, baseline subtraction is performed between spatiallyregistered images. In some embodiments, other forms of baselining areperformed and, generally, baselining may involve any suitablemathematical function and is not limited to subtraction.

Baselining may suppress manufacturing variations while enhancing theobservability of flaws in the component. For example, manufacturingvariations may produce changes in an observable material property (e.g.,conductivity) that are on the same order as changes produced from, say,impact damage. Baseline subtraction will enable the impact damage to beobserved, because of the change in properties between the initialinspection data and the later inspection data. The manufacturingvariations in a component will not have changed, however, and thus willbe suppressed by baseline subtraction. In one such embodiment,subtraction of a previous image (spatially registered to the first imagefrom the same digital NDT method) other than the baseline is performedto enhance noise suppression or improve crack detection and crack growthrate estimation. In one such embodiment, combinations of two or moreimages are used to create a functional value of each image location thatis then used for estimation and prediction. Where the functional valuederived from the data at the same location in two or more images. Thefunctional value is also derived at additional locations within at leasttwo images.

To perform the baseline subtraction the earlier inspection data may besubtracted from later inspection data on a point-by-point basis. In someembodiments the resolution and/or spatial position of the samples may bedifferent between the sets of inspection data. Any suitableinterpolation method may be used to produce the difference. In someembodiments, the initial inspection data captured at step 501 is used asthe baseline to which all future inspection data is compared. In someembodiments, the inspection immediately preceding the current inspectionis used as the baseline. Though, any suitable inspection data may beused as a baseline.

Plot 700, shown in FIG. 7A, illustrates the use of baseline subtractionto enhance the visibility of a crack in a titanium alloy (Ti-6Al-4V).Curve 701 shows the normalized conductivity after 15,000 stress cycles.Curve 703 shows the normalized conductivity after 21,000 stress cycles.Both curves 701 and 703 are obtained by averaging 5 repeat scans using aMWM sensor at the respective time. Plot 710, shown in FIG. 7B, shows thechange in conductivity curve 711 between 15,000 and 21,000 cycles. Thedrop in conductivity from the baseline level at around 0.52 inchescreates a indicator for a crack that would not be directly identifiedfrom curve 703 alone.

It should be appreciated that the operation of baseline subtractioncomputes the change of the material properties. Knowledge of the timedifference between the current inspection and the inspection data usedas the baseline (where the baseline is taken from either from digitalNDT data at t0 or some other earlier time) may be used to estimate therate of change in material properties; that is the first derivative. Itshould also be appreciated that as more inspection data becomesavailable, for example after each inspection time, higher orderderivatives may be estimated. For example, after data from a thirdinspection becomes available, the rate of change (first derivative) maybe estimated using the first in-service inspection and the initialinspection and may again be estimated using the first and secondin-service inspection. Accordingly, the second derivate, that is therate of change in the rate of change, may be estimated. Further, as moreinspection data becomes available, the estimates may be refined.

At step 515, the inspection data is filtered using a signature from asignature library. As discussed above, the signature may be obtainedfrom coupon tests of known flaws. In some embodiments, the inspectiondata is searched for a match to each signature. A match may have thesame shape as the signature. A threshold may be set to determine whethera match has been found. If the same location on a component matchesmultiple signatures, the best match may be chosen for that location.Signatures may be matched at multiple locations on a component. Applyingsignatures to inspection data results in a POD curve that is steeperthan for typical testing methodologies. In other words, flaw sizes belowthe desired detection threshold are suppressed, while flaw sizes above adesired threshold are detected more readily. In one such embodiment, afunction of multiple signatures, perhaps at different frequencies or fordifferent crack sizes, is used to filter the inspection data.

At step 517, the current condition of the component is estimated. Thecurrent condition may be estimated by characterizing the (filtered)sensor response and using the characterization to look-up the componentcondition. In some embodiments the sensor response is characterized by afeature height, a feature area, a half-height width, a crackcorrelation, or in any other suitable way. The feature height may bedefined as the peak change in response at a feature relative to thesurrounding response. The half-height width may be defined as the widthof the feature at half the height. To illustrate, plot 800, shown inFIG. 8A, sketches a sensor response 801 near a feature. Height 803 isthe change in sensor response from line 805 to point 807. Thehalf-height width 809 is the distance across the feature at half way upthe height 803. These metrics for characterizing a feature observed ininspection data are illustrative. It should be appreciated that anysuitable metric may be used to characterize inspection data.

Once the inspection data is characterized, a mapping may be used todetermine the component condition. In some embodiments, the mapping isdetermined experimentally. For example, the sensor response may bemeasured and characterized for various damage feature sizes in a coupontest. This data may be used to determine the condition of a component byusing the sensor response on the component to compute the distributionof crack sizes that is most likely to have produced the sensor response.

FIG. 8B shows a plot 810 of example data for a coupon test. Axis 811represents the characterized sensor response, â (“a hat”). Axis 813represents a characteristic of the flaw. For example, the characteristicof a crack may be the crack width, crack depth, crack length, crackvolume, or any other suitable characteristic or combination ofcharacteristics. In some embodiments, “a” represents the density ofcracks. Coupon data 814, represented by the square blocks, may beobtained by performing sensor measurements on flaws that have beencharacterized using a secondary measurement technique. From the coupondata the correlation between the sensor characteristic response and thecharacteristic of the flaw may be determined. From the sample data,probability distribution functions may be estimated both for “a” and â.

Also shown on plot 810 is a sensor response 815 for a flaw with anunknown characteristic size, “a”. Using the sample data the expectedvalue of the flaw size, “a” may be determined for the sensor response815. Superimposed on plot 810 is a probability density function 816representing the probability density 817 of the different flaw sizecharacteristics. For illustrative purposes, sensor response 815 isplotted along axis 813 at the expected value for “a”.

In some embodiments, the flaw may be too small to reliably detect usingonly the inspection data from the current inspection. To determinewhether the flaw detected is reliable a threshold may be set for thelikelihood that the flaw is smaller than a certain size. For example, itis determined that insufficient information exists to reliably detect aflaw using the current inspection data if the probability of detectingthe flaw is below 90%. When insufficient information exists to reliablydetect the flaw using the inspection data from the current time, anenhanced response from the inspection may be generated by usinginspection data from the current inspection and one or more previousinspection times.

Returning to method 500, at step 519 the future condition of thecomponent is predicted. In some embodiments, the future condition ispredicted at a proposed next inspection time. In some embodiments, thefuture time at which the component condition will have deteriorated to acertain point is predicted. In some embodiments, the method produces arisk of failure as a function of subsequent usage cycles. The predictionmade at step 519 may produce a maximum likelihood value and anuncertainty value. In some embodiments, the prediction is simplydescribed by a probability distribution function for the futurecondition or future time.

Prediction of the future condition may be facilitated by using amechanism other than direct execution of the phenomenological model. Forexample, a precomputed database such as the condition progressiondatabase 245 (FIG. 2) may be used. In some embodiments, use of aprecomputed database allows for real time determination of the futurecondition, while use of the phenomenological model to predict the futurecondition may take a considerably longer time. Here, real time isunderstood to be a time period of a few minutes. For example, twominutes or less. Though, in some embodiments, a real time prediction ofthe future condition may be a table look-up from the precomputeddatabase in a few to several seconds.

In some embodiments, the estimated current condition and estimatedoperating condition of the component are described probabilistically.That is, an uncertainty may be associated with the values. If inspectiondata from multiple inspection data is available, the condition at therespective inspection times may be described probabilistically.Accordingly, the output future condition of the component may also bedescribed probabilistically. A hyperlattice that may be used to accountfor uncertainty may also be referred to as a fuzzy hyperlattice.

In some embodiments, the estimated current condition, one or moreestimated and then predicted operating conditions, including thepredicted number of equivalent cycles at the next inspection time areused to predict the future condition. Though, any suitable inputs may beused to predict the future condition. Each of these input parameters maybe described probabilistically as shown by plots 901-911 in FIG. 9A.Specifically, plots 901, 903, and 905 show example sketches ofprobability density functions for the estimated current condition, a;predicted operating conditions, a; and predicted number of cycles at thenext inspection time, c_(t2). The equivalent representation, sketched inplots 907, 909, and 911, respectively, are cumulative distributionfunctions.

The probability distribution of the current condition, “a”, may bedetermined in ways discussed, for example, in connection with step 517.The probability distribution of the predicted operating conditions, σ,may be predicted based on past operating conditions, actual operatingconditions of components in the same pool, a schedule of operations forthe component (or device), fleet history, expert analysis, or in anysuitable way. The probability distribution of the predicted number ofcycles at the next inspection time may be estimated from fleet history,expert analysis, a schedule of operation for the component (or device),or in any suitable way. Of course, if cycles may be measured directlyand operation stopped for inspection after the desired number of cycles,it may be possible that there is little or no uncertainty in the numberof cycles at the next inspection. But, typically the equivalent numberof cycles, i.e., the cycles would be equivalent to a defined number ofcontrolled loading cycles with an assumed spectrum, is not known withlittle or no uncertainty.

As illustrated the block diagram shown in FIG. 9B, the inputs, in thisexample a, σ, and c_(t2), may be input to prediction module 248, whichin turn uses a hyperlattice in condition progression database 245 toestimate the components condition at the next inspection time, a_(t2).FIG. 9C shows a sketch of an example cumulative distribution function ofa_(t2).

The probability distribution of the predicted future condition may bedetermined by performing a series of look-ups in a hyperlattice storedby the condition progression database. In some embodiments, a rapidMonte Carlo method, or other such distribution estimation method, isused to predict the distribution function for the future condition fromthe hyperlattice by randomly selecting the input conditions inaccordance with their respective distribution functions. In oneembodiment, n values (e.g., n=100) are selected for each of the m inputsin accordance with the respective input's distribution function. Then^(m) combinations are input to the hyperlattice to produce n^(m)outputs. Though, the number of samples for each input may be chosen inany suitable way (e.g., independently). The output values describe theprobability distribution of the output variable. The output values maybe represented, for example, as a cumulative distribution function suchas that shown in plot 913 (FIG. 9C). Though, the output values may bepresented in any suitable way.

In some embodiments, the probability distribution of the futurecondition may be estimated by performing multiple look-ups in thehyperlattice where each look-up uses inputs from the distributionfunction of the current and possibly previous conditions of thecomponent. The resulting outputs are weighted in accordance with thelikelihood of the particular input conditions. In this way a probabilitydistribution may be estimated for the future conditions.

In some embodiments, the cumulative distribution functions are dividedinto quantiles as illustrated for plot 907 in FIG. 9A. For example, eachof the m inputs, the respective cumulative distribution function may bedivided into n quantiles (e.g., n=100). As above the n^(m) combinationsare input to the hyperlattice to produce n^(m) outputs which thusrepresent the probability distribution of the output variable.

It should be appreciated that the future condition may be performed foreach indication separately on a component, or the future condition maybe estimated for the entire component. That is, the future condition ofthe component may be determined by predicting the future condition ofeach indication, or the future condition of the component may beestimated taking in account the culmination of indications on thecomponent.

Although, the individual confidence level in the current and/or previouscomponent condition estimates may be below usual POD and PFA rates, thetrend of the condition estimates may provide a reliable basis forestimating future states.

Plot 1000, shown in FIG. 10A, illustrates an operation that may beperformed for the hyperlattice lookup. Specifically, plot 1000 shows theprogressive growth of a flaw (axis 1001) as a function of the number ofcycles (axis 1003) the component was used. The relationship between flawgrowth and usage cycles is predicted for different operating conditions.The current condition of the component is generally referenced by area1010 of plot 1000. The solid lines 1030-1036 represent paths of constantoperating conditions for the component. The lines represent equalprobability quantiles. The dashed lines in area 1010 and area 1020 alsorepresent quantiles for the current and future condition, respectively.It should be appreciated that the smaller the simplex, the higher theprobability the condition falls at that approximate simplex value. Insome embodiments, identifying the future condition comprises identifyingthe smallest simplex. While plot 1000 illustrates a two dimensionalhyperlattice, it should be appreciated that use of quantiles to dividegrids and identify high probability outcomes via the smallest simplexesmay be extended to higher dimensional hyperlattices.

In some embodiments, the probability distribution function of the futurecondition is displayed on a screen for a user to review. In someembodiments, the display is similar to plot 1000. Though, any suitablerepresentation of the future condition may be shown. Additionally, theprobability of failure may be displayed, for example, as show in plot1050 of FIG. 10B. Specifically, plot 1050 shows curve 1051 which is theprobability of failure as a function of the number of cycles. Thecurrent time 1053 and next inspection time 1055 may also be indicated.Though, any suitable representation of the probability of failure may beused.

After predicting the future condition, at step 521, an action isrecommended based on the available information about the component, suchas the estimated current condition and predicted future condition.Though, in some embodiments, the determination at step 521 may be basedonly on current and previous conditions (step 519 omitted). For example,a threshold flaw size may be set and if exceeded by the currentcondition a CBM action is performed (step 523) or the component isretired (step 527).

In some embodiments, the action is determined based on the risk offailure before the next inspection. For example, if the risk of failureis below a first damage tolerance limit, say 0.0001% risk of failurebefore the next inspection, the component may be allowed (method 500continues to step 525). If the risk of failure is above the first damagetolerance limit, but below a second damage tolerance limit, say 0.0005%,the component may be repaired using a CBM action. If the risk of failureis above the second damage tolerance limit, the component may beretired. In some embodiments, the accept/reject/repair decision is basedon the risk of failure before the next inspection or a combination ofthe crack size distribution estimated for the current time and theprojected risk of failure before the next inspection. In someembodiments, the decision is based on the statistical risk forindividual components. In another embodiment, the decision is based onthe risk of failure for a fleet of components based on either 100percent inspection of each component, or inspection of a subpopulationof such components. While yet another embodiment, the crack depth maydetermine whether a CBM action may be allowed along with associatedrisks.

If it is determined at step 521, that a condition based maintenance(CBM) action should be taken, method 500 continues to step 523. At step523 a suitable CBM action is taken. After completing the CBM action,method 500 may return, for example, to step 517 to re-estimate thecurrent condition of the component, predict its future condition, anddetermine whether the CBM achieved the desired affect.

If it is determined to accept the component as is, method 500 continuesto step 525, at which the next inspection time is set. The nextinspection time may be set, for example, in ways similar to thosediscussed in connection with step 505. Though, the additionalinformation obtained through the subsequent inspections may enable thecondition of the component to be projected more accurately.

If it is determined to reject the component, method 500 continues tostep 527. At step 527 the component is retired and method 500 ends.

In some embodiments of method 500, inspection data may be obtained atthe time of inspection (e.g., steps 501, 511) with a load, such asmechanical or thermal loads, intentionally applied to the component. Forexample, a composite propeller might be inspected with a high-resolutionMWM-array with and without a controlled applied load, at two or moredifferent inspection times. The inspection data at each inspection timemay be subtracted for the two different loads (i.e., high load imageminus low load image) and then differenced again in time to obtain animage of the change in the load difference images associated with impactevents. The change in the images may be used as an input for searchingthe hyperlattice and predicting a future condition of the component andthe uncertainty associated with that condition.

Though method 500 has been described for time sequenced inspection data,it should be appreciated that inspection data may be sequenced in anyother suitable way.

While method 500 has been described for a manufactured component, itshould be appreciated that the method may be applied to components forwhich manufacturing data is inappropriate or unavailable. For example, alocal medical condition, such as a tumor or the bond integrity for arepaired joint, may be inspected at an initial time. A subsequentinspection may use the initial inspection as a baseline.

The inventors have further recognized and appreciated that thephenomenological models used to generate hyperlattices may be used forestimation of not only future condition but also the previous conditionof a component. This may be useful when the data has been censored. Thatit, there are gaps in the historical record for a component's life.Censored data may exist, for example due to data loss.

Further, properties of the component at the time of manufacturing may beestimated by determining what initial conditions would lead to theobserved current condition of the component. Such root cause informationmay be useful for determining, for example, material properties at thetime of manufacturing that may only be investigated through expensive ordestructive testing techniques. Accordingly, the framework may be usedto estimate missing data or determine the root cause of the currentconditions.

FIG. 11 shows a flow diagram of a method for adaptively managing thelife of a component according to some embodiments.

A graphical user interface (GUI) that may serve as a front end formethod 500 (FIGS. 5A-5B) is presented with reference to FIGS. 12A-13J.Though, it should be appreciated that any suitable user interface may beused. Further, it should be appreciated that in some embodiments, method500 is automated and may not require regular interaction with anoperator.

The GUI provides an environment for component adaptive life management(CALM). For the purposes of illustrating the CALM environment GUI, anexample of a metal component that develops cracks is discussed. Though,the CALM environment may be used for any suitable type of component orflaw type, or a process other than damage evolution such as heattreatment, forming, machining, curing, welding, or a medical procedureprogression.

According to some embodiments, the CALM environment is implemented byone or more modules. The modules that are used during inspection of acomponent may be implemented to operate within a data acquisition andprocessing application such as the GridStation™ environment availablefrom JENTEK Sensors Inc., Waltham, Mass. The modules may include asupervisor module that guides the operator through the process, and oneor more plug-in modules that may implement, for example, dataprocessing, statistical analysis, and automatic report generation.

According to some embodiments, there are several plug-ins that implementvarious stages of the data processing. A plug-in named “FindIndications” may be used at the baseline (t0) stage and it identifiesthe locations and magnitudes of indications based on changes in themeasured material property, for example, a localized drop inconductivity.

A plug-in named “Find Indications 2” may be used at the t1 stage of theinspection process. Find Indications 2 finds indications after baselinesubtraction of the baseline data taken at t0 and uses shape filtering,for example, using signatures from signature library 244 (FIG. 2).

A plug-in named “CALM CDF(a)” may be run after Find Indications 2. Foreach indication identified by the plug-in “Find Indications 2”, CALMCDF(a) uses “â vs. a” statistical analysis to compute a cumulativedistribution function for the crack size at this indication at time t1(i.e., cdf(a)|t1). CALM CDF(a) then runs this CDF, together with CDFs onstress and usage cycles, through an appropriate hyperlattice in twoseparate ways: (1) generate cdf(a)|t2 that computes the expected cracksize distribution at this location at a future time t2 given by theCDF(usage) provided; and (2) generate cdf(usage)|a2 that computes theprobability distribution of usage cycles for the crack at this locationto grow to a predetermined threshold size.

A “Reporting” plug-in may be used to automatically generate reportsbased on the outputs from the other plug-ins.

The supervisor module may generate the GUI and other visual elements ofthe software environment encountered during an inspection. An operatorwill begin with the window 1200 shown in FIG. 12A. Here there are threelinks to choose between, depending on whether this is a baseline scan(t0), a first inspection scan (t1), or a subsequent inspection scan(t2+).

If the operator clicks on the Baseline Inspection link in window 1200,he is shown the steps that to be completed in a baseline inspection, asshown in window 1201, FIG. 12B. The next step is shown in bold and witha yellow arrow. This is the step that will also be reached by clickingon the “Next” button.

In this step the operator is asked to fill in component metadata, asshown in window 1203, FIG. 12C. If the operator clicks on the purpleaction button, the metadata table in GridStation opens (unless alreadyopen). An example of metadata in shown in table 1205, FIG. 12D. Theoperator may fill out the second column of table 1205. The fields inthis table may be customizable. The metadata in table 1205 may be savedwith any data acquired as part of the inspection and is also included inthe automatically generated reports.

After the operator fills out the metadata table, he is taken back to thelist of steps, as shown in window 1207, FIG. 12E.

The next step in the procedure is to acquire the baseline scan data onthe component. The supervisor provides the operator with a set ofinstructions, as shown in window 1209, FIG. 12F.

After the scan data is acquired, the operator is instructed to save thedata, as shown in windows 1211 and 1213 of FIG. 12G and FIG. 12H,respectively. When the operator clicks on the “Record baseline data” inwindow 1213, he is presented with a dialog to save the baseline data.

After the data has been acquired and saved, it is time to run thebaseline indications algorithm (the plug-in named “Find Indications”) asshown in window 1215, FIG. 12I and window 1217, FIG. 12J. The algorithmbegins data processing after the operator clicks on the “Run Baselinedata algorithm” shown in window 1217.

After the plug-in has finished executing, the data is presented invisual form as C-scans, as shown in the screen-dump in window 1221, FIG.12L. These C-scan images may also be included in the automaticallygenerated report. In window 1223, FIG. 12M, the operator is presentedwith a table that shows a list the most likely indications, asdetermined by the Find Indications module. This is shown in window 1219,FIG. 12K. The table lists the physical location of the indications, themagnitudes (â), and the status. The status may be either “Reject” or“Track”, based on whether the indication is above a certain thresholdthat may be specified as part of the plug-in configuration and includedin the automatically generated reports. In window 1219, the operator hasthe opportunity to change the status of the indications, or to set thestatus to “Invalid” which is used to let the environment know that thisindication should not be retained for further tracking. The operator canalso enter comments for each indication, which are retained with thedata. After this the operator is asked to validate the list ofindications by clicking on the “Validate button”.

If the status of any of the indications in the table in window 1219 are“Reject” after validation by the operator, then the supervisor moduleinforms the operator that the component has been rejected and promptshim to create an NDT report, as shown in windows 1223 and 1225, FIG. 12Mand FIG. 12N, respectively. If this is the case, this completes theinspection of this component and the operator is shown the screen inwindow 1238, FIG. 12R.

If, on the other hand, none of the indications have a “Reject” status,the operator is given the next set of steps, as shown in window 1227,FIG. 12O. These steps include saving the results of the data analysisfor future inspections (window 1229, FIG. 12P) and generating an NDTreport (window 1231, FIG. 12Q). After these steps are completed thebaseline scan stage of the inspection is complete and the operator isshown the screen in window 1238, FIG. 12R.

Clicking on “Create NDT report” button in window 1227 (FIG. 12O) runsthe reporting plug-in which automatically generates an appropriatereport.

After the operator clicks on the First Inspection (t1) link in window1201, FIG. 12A, he is shown the steps that must be completed in aninspection at time t1, assuming that data from a baseline scan isavailable, as shown in window 1235, FIG. 12S.

In this case no metadata is required of the operator, because it wasalready filled out at the time of the baseline scan. The operator is,however, always able to edit the data in the metadata table and theedited date will be saved in future data files and included inautomatically generated reports.

Windows 1237, 1239 and 1241 (FIGS. 12T-12V) walk the operator though thesteps to take a scan on the component and store the scan data. Thesesteps are similar to the steps in the baseline stage, describedpreviously.

After the data has been acquired and saved, it is time to run the dataprocessing and statistical algorithms (the plug-ins named “FindIndications 2” and “CALM CDF(a)”) as shown in windows 1243 and 1245 ofFIG. 12W and FIG. 12X, respectively. The algorithms begin dataprocessing after the operator clicks on the “Run Algorithm” button shownin window 1245, FIG. 12X.

After the plug-ins have finished executing, the data may be presented invisual form as C-scans and statistical CDF function curves, as shown inthe screen-dumps in window 1247, FIG. 12Y and window 1249, FIG. 12Z.Note that for clarity in these figures some of the windows have beenhidden (including the supervisor window) so that the data views can beshown. These C-scan and graph images may also be included in theautomatically generated report. Within the supervisor window, theoperator is presented with a table that shows a list of the top fivemost likely indications, as determined by the algorithm. This is shownin window 1301, FIG. 13A. The table lists the physical location of theindications, the magnitudes (â), and the status. The status can beeither “Reject” or “Track”, based on whether the indication is above acertain threshold, specified as part of the plug-in configuration andincluded in the NDT reports. In the screen shown in window 1301, theoperator has the opportunity to change the status of the indications, orto set the status to “Invalid” which is used to let the software knowthat this indication is not “real” and should not be retained forfurther tracking. The operator can also enter comments for eachindication, which are retained with the data. After this the operator isasked to validate the list of indications by clicking on the “Validatebutton”.

If the status of any of the indications in the table in window 1301 are“Reject” after validation by the operator, then the supervisor informsthe operator that the component has been rejected and prompts him tocreate an NDT report, as shown in window 1303, FIG. 13B and window 1305,FIG. 13C. If this is the case, this completes the inspection of thiscomponent and the operator is shown the screen in window 1317, FIG. 13I.

If, on the other hand, none of the indications have a “Reject” status,the operator is given the next set of steps, as shown in window 1307,FIG. 13D. These steps include saving the results of the data analysisfor future inspections (window 1307, FIG. 13D and window 1309, FIG.13E), generating an NDT report (window 1305, FIG. 13C), and setting thenext inspection interval based on the statistical analysis through thefuzzy lattice.

After these steps are completed the baseline scan stage of theinspection is complete and the operator is shown the screen in window1317, FIG. 13I. After finishing work with the supervisor, the operatoris instructed that the process is over (window 1319, FIG. 13J).

As already discussed, for each indication identified by the plug-in“Find Indications 2”, the plugin “CALM CDF(a)” uses the “â vs. a”statistical analysis to compute a cdf(a)|t1 cumulative distributionfunction (CDF) for the crack size at this indication. This result isshown as a separate curve for each indication, as seen in window 1249,FIG. 12Z (upper left). This analysis uses a vs. a data gathered as partof this effort on Titanium alloy coupons and the statistical data thatcharacterize this correlation are input as part of the plug-inconfiguration.

It then runs this CDF, together with CDFs on stress and usage, throughthe fuzzy lattice to generate cdf(a)|t2 that computes the expected cracksize distribution at this location at a future time t2 given by theCDF(usage) provided. This result is shown in the curves in window 1249,FIG. 12Z (lower left). In the example presented here, the stress andusage input CDF distributions were assumed to be normal, with means andstandard deviations as shown in the plug-in configuration, in this caseset to 415±42 ksi and 2000±200 cycles respectively. The plug-in allowsfor non-normal distributions to be included as separate data files.

The plug-in also generates cdf(usage)|a2 that computes the probabilitydistribution of usage cycles for the crack at this location to grow to apredetermined threshold crack size. This threshold crack size is part ofthe plug-in configuration, set to 79 mils (2 mm) in this example. Theresults of this analysis are shown in the curves in window 1249 of FIG.12Z (lower right). This CDF(usage) distribution for the highest rankingindication (indication 1) is what is used to set the next inspectioninterval, as indicated in window 1315, FIG. 13H, given a tolerable risklevel for failure before the next inspection.

Clicking on the “Create NDT report” button in window 1305, FIG. 13C runsthe reporting plug-in which automatically generates a report such as aWord document.

Flaw Size Distribution Inferred From NDT Inspection Results

A mean relationship between NDT signal and flaw sizes is establishedutilizing coupon data. However, individual flaw signals will vary aboutthat mean relationship. Thus, from a population of flaws of the samesize a distribution of sensor measurement signals would be produced.Although from the same size flaw, if the mean relationship was used foreach of those signals to estimate a corresponding flaw size, theresulting estimated flaw sizes would be distributed about the actualflaw size. The process developed and specified here may be used toquantify the resulting uncertainty in estimating flaw sizes that isinduced by signal variation. Though, uncertainty may be quantified inany suitable way.

The general technique of quantifying probability of detection (POD) foran NDE process based on signal data is referred to as an “a-hat” versus“a” analysis. This nomenclature comes out of the first presenters of themethodology using the variable “a” to refer to flaw size with “a-hat”referring to the signal data. The methodology is that of regression inwhich the signal is related to the flaw size through some relationship.The most commonly used relationship is that that, on average, thelogarithm of the signal has a linear relationship with the logarithm ofthe flaw size. That is,

E[ ln(S)]=β₀+β₁·ln(a),  (1)

where S denotes the signal (often written ^(â), thus the name a-hat) andE is the expectation operator.

Equation (1) is not enough to quantify the reliability associated withthe NDE process, as it only models an average relationship of signalwith flaw size. A full specification of the distribution of the signalmay be modeled by adding an error term that captures the differencebetween the signal relationship and the mean line. That is,

ln(S)=β₀+β₁·ln(a)+∈,  (2)

where ∈ is now a random variable with mean 0. The full probabilisticnature of the signal in this representation is captured in the meanβ₀+β₁·ln(a) and the distribution assigned to the zero mean randomvariable ∈.

The assumption that ∈ has a Gaussian distribution with mean 0 andvariance δ² is the usual basis of analysis that yields the equivalenceof the maximum likelihood estimates (MLE) for β₀ and β₁ the leastsquares estimates. Although the above model has served well to capturethe behavior of many reliability characterizations, it is worth notingthat the assumptions do not have to be restricted to those given above.The problem may be generalized to

g _(S)(S)=β₀+β₁ ·g _(A)(a)+∈,  (3)

where g_(S)(·) and g_(A)(·) are increasing functions with inverses g_(S)⁻¹ and g_(A) ⁻¹, and ∈ is a zero mean random variable with probabilitydensity function ƒ_(S)(·). With this formulation it is assumed thatneither of the functions g_(S)(·) and g_(A)(·) have parameters in needof estimation from the data. Estimates β₀, β₁ and any additionalparameters defining f_(S)(·) can be estimated from n data pairs{(a_(i),s_(i)),i=1, . . . , n} of flaws sizes and signals by the maximumlikelihood (ML) method. That is, let θ be the vector of parametersneeded to fully specify the density f_(S)(·), then the ML estimates aregiven by {circumflex over (β)}₀, {circumflex over (β)}₁, and {circumflexover (θ)} which are the solutions to

$\max\limits_{\beta_{0},\beta_{1},\theta}{\prod\limits_{i = 1}^{n}\left\{ {f_{S}\left( {{g_{S}\left( s_{i} \right)} - \left\lbrack {\beta_{0} + {\beta_{1} \cdot {g_{A}(a)}}} \right\rbrack} \right)} \right\}}$

Letting x=g_(A)(a) and y=g_(S)(S) and f_(S)(x)=(√{square root over(2π)})⁻¹e^(x) ² ^(/2) then equation (3) is the usual linear regressionwith Gaussian assumption for the errors given as

y=β ₀+β₁ ·x+∈.  (4)

In this case the ML estimates and the least square linear regressiongive the same estimates.

Equation (4) is written as a function of the signal having a meandepending on the flaw size with probabilistic variation around thatmean. In designing POD quantification experiments the flaw sizes may beset and signals measured corresponding to those individual flaws. It isthus appropriate for the error structure in the model to be associatedwith the signal measurement. However, once the relationship of signal toflaw size is estimated we can ask the inverse question of what is thebest guess for the flaw size that corresponds to a measured signal notincluded in the original data set.

There are two general approaches to estimating the flaw sizecorresponding to a subsequently measured signal, s′, following the“calibration” step. The classical approach is to simply solve the meanequation in terms of the flaw size. That is, set

$x^{\prime} = {\frac{y^{\prime} - {\hat{\beta}}_{0}}{{\hat{\beta}}_{1}}.}$

This is equivalent to reading of the flaw value corresponding to a givensignal from the mean line previously fitting the signal relationship tothe flaw size. The second approach is to recast the problem as if theregression was for determining the flaw size while treating the signalas the independent variable. That is, find the coefficients for theregression

x=γ ₀+γ₁ ·y+∈.  (5)

and then set

It should be noted that these two approaches are not equivalent. That is{circumflex over (γ)}₁≠1/{circumflex over (β)}₁, nor is

≠

We will follow the classical approach as it also provides the maximumlikelihood estimate for the unknown flaw size in the Gaussian models. Tosee this we consider the set of n data pairs {(x_(i),y_(i)),i=1, . . . ,n} of flaws sizes and signals (or appropriate functions of them) as wellas one additional signal y_(n+1) y_(n+1) for which the correspondingflaw size, x_(n+1), is unknown. Using the regression model (4) andmaking the Gaussian assumption that ∈≈N(0,σ²) we write the likelihoodfunction as

$L = {\prod\limits_{i = 1}^{n + 1}{\frac{1}{\sqrt{2\pi \; \sigma^{2}}}{\exp \left( {{- \frac{1}{2\sigma^{2}}}\left( {y_{i} - \beta_{0} - {\beta_{1} \cdot x_{i}}} \right)^{2}} \right)}}}$

Hence the log likelihood is given by

$\begin{matrix}{{{LL}\left( {\beta_{0},\beta_{1},\sigma,x_{n + 1}} \right)} = {{{- \frac{n + 1}{2}}{\ln \left( {2\pi} \right)}} - {\left( {n + 1} \right){\ln (\sigma)}} - {\frac{1}{2\sigma^{2}}{\sum\limits_{i = 1}^{n + 1}\left( {y_{i} - \beta_{0} - {\beta_{1} \cdot x_{i}}} \right)^{2}}}}} & (6)\end{matrix}$

The parameters that the log likelihood would be maximized over to givean MLE are shown in the argument list.

Initially we will treat x_(n+1) as known, as in that case we know themaximum likelihood estimates for the other parameters. Specifically theyare given in terms of the following statistics.

${S_{xy} = {\frac{1}{n + 1} \cdot {\sum\limits_{i = 1}^{n + 1}{\left( {x_{i} - \overset{\_}{X}} \right) \cdot \left( {y_{i} - \overset{\_}{Y}} \right)}}}},{S_{x}^{2} = {\frac{1}{n + 1} \cdot {\sum\limits_{i = 1}^{n + 1}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}},{and}$$S_{y}^{2} = {\frac{1}{n + 1} \cdot {\sum\limits_{i = 1}^{n + 1}\left( {y_{i} - \overset{\_}{Y}} \right)^{2}}}$

where and X and Y are the means of the x and y data. We also write

$r = {\frac{S_{xy}}{S_{x} \cdot S_{y}}.}$

It is well known that the maximum likelihood estimates are given by

${{\hat{\beta}}_{1} = {{\frac{S_{y}}{S_{x}} \cdot r} = \frac{S_{xy}}{S_{x}^{2}}}},\mspace{14mu} {{\hat{\beta}}_{0} = {\overset{\_}{Y} - {{\hat{\beta}}_{1} \cdot \overset{\_}{X}}}},{{{and}\mspace{14mu} {\hat{\sigma}}^{2}} = {\frac{1}{n + 1}{\sum\limits_{i = 1}^{n + 1}\left( {y_{i} - {\hat{\beta}}_{0} - {{\hat{\beta}}_{1} \cdot x_{i}}} \right)^{2}}}}$

Making the substitutions back into equation (6) we see that

${LL} = {{{- \frac{n + 1}{2}}{\ln \left( {2\pi} \right)}} - {\left( {n + 1} \right){\ln \left( \hat{\sigma} \right)}} - \frac{n + 1}{2}}$

and that the log likelihood is maximized when the estimated variance isminimized. Thus, assuming that x_(n+1) is known we know that theparameter estimates that maximizes the likelihood also minimizes{circumflex over (σ)}². Note that

${\hat{\sigma}}^{2} = {{\frac{n}{n + 1}\left( {\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {y_{i} - {\hat{\beta}}_{0} - {{\hat{\beta}}_{1} \cdot x_{i}}} \right)^{2}}} \right)} + \frac{\left( {y_{n + 1} - {\hat{\beta}}_{0} - {{\hat{\beta}}_{1} \cdot x_{n + 1}}} \right)^{2}}{n + 1}}$

We know that the first term on the right hand side is minimized bysetting {circumflex over (β)}₀ and

to the solutions based on the first n data points. The contribution ofthe x_(n+1) term can be made 0 by letting

${\hat{x}}_{n + 1} = {\frac{y_{n + 1} - {\hat{\beta}}_{0}}{{\hat{\beta}}_{1}}.}$

Not done here, but with a little algebra it can be shown that the MLEestimates for the parameters based on the n+1 data pairs

$\left\{ {\left( {x_{i},y_{i}} \right),{i = 1},\ldots \mspace{14mu},n,\left( {\frac{y_{n + 1} - {\hat{\beta}}_{0}}{{\hat{\beta}}_{1}},y_{n + 1}} \right)} \right\}$

are the same as those based on just the first n data pairs, where theflaw sizes are all known.

It should be noted that not only is the estimator for x_(n+1) given by

$\frac{y_{n + 1} - \beta_{0}}{\beta_{1}}$

not unbiased, that in fact the distribution does not have a finitevariance nor mean. Thus the usual method of confidence intervals usingthe estimated value plus or minus an appropriate multiple of thestandard error cannot be applied. There are several approaches one cantake to provide reasonable confidence limits for the unknown flaw sizecharacteristic, x_(n+1). One that we develop here is to write out thedistribution theory for y_(n+1) as if x_(n+1) is known and y_(n+1) is arandom variable. Developing this theory we can write the confidencestatement that holds for y_(n+1) which is a function of x_(n+1), butinstead of constructing the interval for the signal we treat the signalas given and instead write the interval in terms of the x_(n+1).

Here we give the results utilizing the following terms:

The percentile of the t distribution with n-2 degrees of freedom andupper tail probability of α/2 is given by t_(a/2:n−2)The mean of the signal data is

$\overset{\_}{Y} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}y_{i}}}$

The mean of the flaw data is

${\overset{\_}{X} = {{\frac{1}{n}{\sum\limits_{i = 1}^{n}{x_{i}.{\hat{\beta}}_{1}}}} = \frac{\sum\limits_{i = 1}^{n}{\left( {x_{i} - \overset{\_}{X}} \right) \cdot \left( {y_{i} - \overset{\_}{Y}} \right)}}{\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}},$

and {circumflex over (β)}₀= Y−{circumflex over (β)}₁· X

${\hat{\sigma}}^{2} = \frac{\sum\limits_{i = 1}^{n}\left( {y_{i} - {\hat{\beta}}_{0} - {{\hat{\beta}}_{1} \cdot x_{i}}} \right)^{2}}{n - 2}$

is the unbiased estimate for the variance and

$a = {{\hat{\beta}}_{1}^{2} - \frac{{\hat{\sigma}}^{2}t_{{\alpha/2};{n - 2}}^{2}}{\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}$

Using the above values determined from a “calibration” run the followingprocedure is used to estimate the flaw size from an unknown flaw sizeproducing an observed signal of y_(n+1)

1. Estimate of x_(n+1) is given by

${\hat{x}}_{n + 1} = {\frac{y_{n + 1} - {\hat{\beta}}_{0}}{{\hat{\beta}}_{1}} = {\overset{\_}{X} + \frac{y_{n + 1} - \overset{\_}{Y}}{{\hat{\beta}}_{1}}}}$

2. To obtain a 1−α^(1−α) confidence limit for x_(n+1) have to assurethat the 1−α confidence limit for β₁ does not include 0. Thus test thehypothesis, HO: β₁=0 versus the alternative, Ha: β₁≠0 with a size αtest. That is reject HO if and only if

$\frac{{\hat{\beta}}_{1}^{2} \cdot {\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}{{\hat{\sigma}}^{2}} \geq t_{{\alpha/2};{n - 2}}^{2}$

3. If HO is not rejected then the confidence interval for x_(n+1) wouldbe infinite as there is not enough evidence that a dependency betweensignal and flaw size exists.4. A rejection of the null hypothesis in step 2 assures the existence ofa finite 100(1−α)% confidence interval for x_(n+1)

${Lower} = {\overset{\_}{X} + \frac{{\hat{\beta}}_{1}\left( {y_{n + 1} - \overset{\_}{Y}} \right)}{a} - {\frac{\hat{\sigma} \cdot t_{{\alpha/2};{n - 2}}}{a}\sqrt{{a\left( \frac{n + 1}{n} \right)} + \frac{\left( {y_{n + 1} - \overset{\_}{Y}} \right)^{2}}{\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}}}$and${Upper} = {\overset{\_}{X} + \frac{{\hat{\beta}}_{1}\left( {y_{n + 1} - \overset{\_}{Y}} \right)}{a} + {\frac{\hat{\sigma} \cdot t_{{\alpha/2};{n - 2}}}{a}\sqrt{{a\left( \frac{n + 1}{n} \right)} + \frac{\left( {y_{n + 1} - \overset{\_}{Y}} \right)^{2}}{\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{X}} \right)^{2}}}}}$

The endpoints constituting the interval are not necessarily equidistantfrom the point estimate.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those skilled inthe art.

Such alterations, modifications, and improvements are intended to bepart of this disclosure, and are intended to be within the spirit andscope of the invention. Accordingly, the foregoing description anddrawings are by way of example only.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers.

Further, it should be appreciated that a computer may be embodied in anyof a number of forms, such as a rack-mounted computer, a desktopcomputer, a laptop computer, or a tablet computer. Additionally, acomputer may be embedded in a device not generally regarded as acomputer but with suitable processing capabilities, including a PersonalDigital Assistant (PDA), a smart phone or any other suitable portable orfixed electronic device.

Also, a computer may have one or more input and output devices. Thesedevices can be used, among other things, to present a user interface.Examples of output devices that can be used to provide a user interfaceinclude printers or display screens for visual presentation of outputand speakers or other sound generating devices for audible presentationof output. Examples of input devices that can be used for a userinterface include keyboards, and pointing devices, such as mice, touchpads, and digitizing tablets. As another example, a computer may receiveinput information through speech recognition or in other audible format.

Such computers may be interconnected by one or more networks in anysuitable form, including as a local area network or a wide area network,such as an enterprise network or the Internet. Such networks may bebased on any suitable technology and may operate according to anysuitable protocol and may include wireless networks, wired networks orfiber optic networks.

Also, the various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of a number of suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a framework or virtual machine.

In this respect, the invention may be embodied as a computer readablemedium (or multiple computer readable media) (e.g., a computer memory,one or more floppy discs, compact discs, optical discs, magnetic tapes,flash memories, circuit configurations in Field Programmable Gate Arraysor other semiconductor devices, or other tangible computer storagemedium) encoded with one or more programs that, when executed on one ormore computers or other processors, perform methods that implement thevarious embodiments of the invention discussed above. The computerreadable medium or media can be transportable, such that the program orprograms stored thereon can be loaded onto one or more differentcomputers or other processors to implement various aspects of thepresent invention as discussed above.

In this respect, it should be appreciated that one implementation of theabove-described embodiments comprises at least one computer-readablemedium encoded with a computer program (e.g., a plurality ofinstructions), which, when executed on a processor, performs some or allof the above-discussed functions of these embodiments. As used herein,the term “computer-readable medium” encompasses only a computer-readablemedium that can be considered to be a machine or a manufacture (i.e.,article of manufacture). A computer-readable medium may be, for example,a tangible medium on which computer-readable information may be encodedor stored, a storage medium on which computer-readable information maybe encoded or stored, and/or a non-transitory medium on whichcomputer-readable information may be encoded or stored. Othernon-exhaustive examples of computer-readable media include a computermemory (e.g., a ROM, a RAM, a flash memory, or other type of computermemory), a magnetic disc or tape, an optical disc, and/or other types ofcomputer-readable media that can be considered to be a machine or amanufacture.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present invention asdiscussed above. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs thatwhen executed perform methods of the present invention need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present invention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in computer-readable media in anysuitable form. For simplicity of illustration, data structures may beshown to have fields that are related through location in the datastructure. Such relationships may likewise be achieved by assigningstorage for the fields with locations in a computer-readable medium thatconveys relationship between the fields. However, any suitable mechanismmay be used to establish a relationship between information in fields ofa data structure, including through the use of pointers, tags or othermechanisms that establish relationship between data elements.

Various aspects of the present invention may be used alone, incombination, or in a variety of arrangements not specifically discussedin the embodiments described in the foregoing and is therefore notlimited in its application to the details and arrangement of componentsset forth in the foregoing description or illustrated in the drawings.For example, aspects described in one embodiment may be combined in anymanner with aspects described in other embodiments.

Also, the invention may be embodied as a method, of which an example hasbeen provided. The acts performed as part of the method may be orderedin any suitable way. Accordingly, embodiments may be constructed inwhich acts are performed in an order different than illustrated, whichmay include performing some acts simultaneously, even though shown assequential acts in illustrative embodiments.

Use of ordinal terms such as “first,” “second,” “third,” etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed, but are usedmerely as labels to distinguish one claim element having a certain namefrom another element having a same name (but for use of the ordinalterm) to distinguish the claim elements.

Embodiments described herein are related to the Application filedconcurrently herewith, bearing Attorney Docket Number 1884.2073-001,entitled “Component Adaptive Life Management,” of Goldfine et al., theentire disclosure of which is hereby incorporated herein by reference.

Also, the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having,” “containing,” “involving,” andvariations thereof herein, is meant to encompass the items listedthereafter and equivalents thereof as well as additional items.

1. A computer-readable storage medium comprising computer-executableinstructions that, when executed by at least one processor, perform amethod comprising acts of: receiving at least two sets of sensor data,each of the at least two sets of sensor data comprising spatial data fora measured material condition of a component; spatially registering theat least two sets of sensor data with respect to each other and thecomponent; computing a change in the material condition of the componentfrom the spatially registered at least two sets of sensor data;estimating the current condition based at least in part on the change inthe material condition; and predicting a future condition of thecomponent at a future time based at least in part on the estimatedcurrent condition, the future condition of the component being predictedusing a database comprising a plurality of precomputed materialconditions of the component, each precomputed material conditioncomputed for a respective operating condition and time; the methodfurther comprising generating the precomputed material conditions usinga flaw growth model; storing the precomputed material conditions in thedatabase; filtering at least one of the at least two sets of sensor datawith at least one flaw signature; and estimating a current condition ofthe component from the filtered sensor data, and a stored database ofhistorical sensor data from a simple element selected to represent thecomponent material and flaw growth behavior.
 2. The computer-readablestorage medium of claim 1, wherein each of a plurality of data points inthe database are generated for a respective combination of an equivalentnumber of fatigue cycles and stress level.
 3. The computer-readablestorage medium of claim 1, wherein the stored database comprises atleast one coupon test representative of the component.
 4. Thecomputer-readable storage medium of claim 1, wherein predicting thefuture condition of the component comprises estimating a service loadingexperienced by the component based at least in part on the change. 5.The computer-readable storage medium of claim 1, wherein the act ofestimating the current condition comprises using the change in materialproperties and archived data, the archived data relating flaw size tosensor signal data.
 6. A method of predicting a risk of failure before afuture time, the method comprising: inspecting a feature of a componentusing a non-destructive testing (NDT) method, wherein the NDT method isperformed at a plurality of inspection times at a plurality of locationson the component, the NDT method producing inspection data for theplurality of locations at each of the plurality of inspection times;storing the inspection data in a computer-readable storage medium;operating at least one processor to determine, based at least in part onthe inspection data, if a damage feature is growing within the componentand, when insufficient information exists to reliably detect the damagefeature using the inspection data at one of the inspection times,generating an enhanced response from the inspection data at two or moreof the inspection times and using a precomputed database with two ormore dimensions as a function of sensed condition and usage that issearched to determine the risk of failure before the future time.
 7. Themethod of claim 6, wherein the enhanced response is a function derivedfrom sensor data at a same location on the component for each of the twoor more inspection times.
 8. The method of claim 7, wherein data atother locations is also used to formulate the function to generateenhanced response.
 9. The method of claim 8, wherein a signature libraryis used to derive the enhanced response.
 10. The method of claim 6,wherein the NDT method is an eddy current array.
 11. The method of claim6, wherein the plurality of locations comprise a fatigue criticallocation on the component, and usage is measured in equivalent fatiguecycles, and the database is generated using a damage evolution model.12. The method of claim 6, wherein: the plurality of inspection timescomprises a first and second time, the first time being a time beforethe component is put into service and the second time being a time afterthe component is put in service, and the inspection data comprises firstinspection data taken at the first time and second inspection data takenat the second time.
 13. The method of claim 6, wherein the flaw is acrack in the component and it is determined that insufficientinformation exists to reliably detect the crack using the inspectiondata at one of the plurality of inspection times if a probability ofdetecting the crack is below a threshold.
 14. The method of claim 13,wherein the threshold is about 90 percent probability of detection, andfailure comprises a size of the crack reaching a critical crack size.15. A method of predicting a future time at which a critical damagelevel will be reached, the method comprising: inspecting a feature of acomponent using a non-destructive testing (NDT) method, wherein the NDTmethod is performed at a plurality of inspection times at a plurality oflocations of the component, the NDT method producing inspection data forthe plurality of locations at each of the plurality of inspection times;storing the inspection data in a computer-readable storage medium;operating at least one processor to determine, based at least in part onthe inspection data, if a damage feature is growing within the componentand, when insufficient information exists to reliably detect the damagefeature using the inspection data at one of the plurality of inspectiontimes, to generate an enhanced response from the inspection data at twoor more of the plurality of inspection times and using a databasegenerated using a model of damage evolution to predict the probabilitydistribution of future times at which the critical damage level will bereached.
 16. The method of claim 15, wherein the future time is measuredin equivalent fatigue cycles, the damage level is crack size, thecritical damage level is a critical crack size, and the location ofinterest on the component is a fatigue critical location.
 17. A methodfor tracking process progression comprising: operating a processor to:process a first inspection image of a component to rank an originalplurality of locations of the component, wherein the original pluralityof locations are ranked based on a quantitative measure that correlateswith predicted crack growth rate at the respective location; filter asecond inspection image of the component using filters devised fromsignatures to suppress indications that are not representative of acondition of interest and enhance the response of conditions that aremore likely to represent the condition of interest; and re-rank theoriginal plurality of locations using the filtered second inspectionimage including additional highly ranked locations, wherein the secondinspection image is acquired at a later time than the first inspectionimage.
 18. The method of claim 17, further comprising: extracting thesignatures from a representative fatigue test article; and storing thesignatures in a signature library on a computer-readable storage medium.19. The method of claim 17, wherein the quantitative measure is a peakconductivity at the respective location.
 20. The method of claim 17,wherein the quantitative measure is a half-height width of conductivitydip at the respective location.
 21. The method of claim 17, wherein thequantitative measure is a peak filter response at the respectivelocation.
 22. The method of claim 17, wherein a fatigue progressiontrack is identified based on a statistically significant trend innon-destructive test (NDT) data from two or more inspection times, wherethe top ranked location is maintained for each inspection until the endof the component's useful life.
 23. The method of claim 22, whereinmultiple NDT passes are recorded at each inspection time.
 24. Acomputer-readable storage medium comprising computer-executableinstructions that, when executed by at least one processor, perform amethod comprising acts of: spatially registering a baseline response ofa component and a current response of the component; after the spatiallyregistering, subtracting the baseline response from the currentresponse; and estimating a probability distribution of a currentcondition of the component by applying a statistical analysis using aset of responses from one or more simplified elements.
 25. Thecomputer-readable storage medium of claim 24, wherein: the baselineresponse is a digital non-destructive test (NDT) image from aninspection performed prior to deployment of the component, the currentresponse is a digital NDT image from an inspection performed afterdeployment and during a service life of the component.
 26. Thecomputer-readable storage medium of claim 24, wherein estimating theprobability distribution of the current condition of the componentcomprises estimating a probability density function.